A driver assistance system supports the driver in driving the vehicle, for example, in observing the selected traffic lane, in an intentional lane change, in observing the safety distance to preceding vehicles, and in driving under poor visual conditions such as at night or in bad weather. Assistance functions such as LDW (Lane Departure Warning), LKS (Lane Keeping Support), LCA (Lane Change Assistant) and ACC (Automatic Cruise Control) are often implemented in a driver assistance system. To detect the surroundings of the vehicle, a driver assistance system of this type includes at least one image sensor such as a mono or stereo camera according to the CCD or CMOS technology, which is typically installed in the vehicle as a forward-looking system. Further sideways-looking or backward-looking image sensors may be installed. In addition, the driver assistance system may include a distance measuring device having radar, lidar, and ultrasound sensors. With the aid of a distance measuring device of this type, the driver assistance system may detect the distance to objects in the surroundings of the vehicle. Other traffic participants in moving or stopped traffic, roadway boundaries, as well as obstacles and the like may be considered as such objects. Velocity values may also be advantageously derived from consecutive distance measurements. To keep the risk in bumper-to-bumper traffic and/or lane change low, the measured values must be detected with the highest possible precision. Methods for deriving a quality measure for the relative velocity of an object which is detected with the aid of a surroundings detection system are already known. The quality measure is generated, for example, from the statistical fluctuations of the historically measured velocity values. This requires considerable computing complexity. In addition, a method of this type yields a result that is useless in practice if only slight fluctuations of the measured value or of the quantity derived therefrom occur. In this case, a relatively high quality measure would be incorrectly ascertained.